Nonlinear Dynamic Characteristics and Four Contact States of a Spur Gear Pair Considered Tooth Profile Error and Extended Tooth Contact

The actual tooth profile of a spur gear will inevitably deviate from the involute tooth profile (ITP) due to machining error, and so on. The nonlinear characteristics and contact state of the gear transmission system will be changed due to tooth profile error, and the system stability will be affected accordingly. A dynamic model of a spur gear pair is established by considering tooth profile error, extended tooth contact, and some time-varying parameters. Tooth profile error and extended tooth contact are directly involved in the calculation of the dynamic meshing force. Besides, the five Poincaré mapping sections Γi and corresponding triggers are established to capture the information on system motion, extended teeth contact, tooth disengagement, and back-side contact. Finally, the bifurcation characteristics and four contact states of the system are studied by using the established Poincaré mapping sections, bifurcation diagrams with multi-mapping sections, and phase portraits. The results indicate that, with the increase of tooth profile error, the system will go through stable periodic motion, alternation between periodic motion and chaotic motion, and unstable chaotic motion. Tooth disengagement and tooth back contact will also occur in turn. The contact of extended teeth is also changed by system bifurcation, tooth disengagement, and back-side contact. This chapter can provide a reference for stability analysis of the gear transmission system.